On the eigenfunctions corresponding to the bandpass kernel, in the case of degeneracy
Author:
J. A. Morrison
Journal:
Quart. Appl. Math. 21 (1963), 13-19
MSC:
Primary 45.12
DOI:
https://doi.org/10.1090/qam/145306
MathSciNet review:
145306
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: It has previously been pointed out that the eigenfunctions of the finite integral equation with bandlimited difference kernel satisfy a certain second order linear differential equation, containing one parameter, whose continuous solutions, for discrete values of the parameter, are the prolate spheroidal wave functions. We consider here the finite integral equation with bandpass difference kernel. It is shown that, in the case of degeneracy, one eigenfunction is the continuous solution of a certain fourth order linear differential equation, containing two parameters which must be determined from prescribed conditions. The second eigenfunction is the derivative of the first one.
D. Slepian, Estimation of signal parameters in the presence of noise, IRE Trans. Infor. Theory, PGIT-3, (1954) 68-89
D. Slepian, private communication
- D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty. I, Bell System Tech. J. 40 (1961), 43–63. MR 140732, DOI https://doi.org/10.1002/j.1538-7305.1961.tb03976.x
J. A. Morrison, On the commutation of finite integral operators, with difference kernels, and linear self-adjoint differential operators.
- Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520
D. Slepian, Estimation of signal parameters in the presence of noise, IRE Trans. Infor. Theory, PGIT-3, (1954) 68-89
D. Slepian, private communication
D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty-I, BSTJ, 40, (1961) 43-64
J. A. Morrison, On the commutation of finite integral operators, with difference kernels, and linear self-adjoint differential operators.
C. Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
45.12
Retrieve articles in all journals
with MSC:
45.12
Additional Information
Article copyright:
© Copyright 1963
American Mathematical Society